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HCF and LCM Word Problems Worksheet

Quantitative aptitude lesson 2: HCF and LCM word problems · Set 121 · 40 questions
TalentJR

The method (LCM or HCF?): Bells, lights, runners “together again”: find the LCM of the gaps. Biggest can, rope piece or tile that fits exactly: find the HCF. Leaves the same remainder r every time: LCM + r. Number of tiles = (length ÷ tile side) × (width ÷ tile side).

NameDateTime takenScore ___ / 40
  1. 1.Saanvi takes 30 seconds and Meera takes 50 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  2. 2.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 5 or 10.
  3. 3.Two tanks hold 90 litres and 20 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  4. 4.A hall floor is 350 cm long and 300 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  5. 5.Two tanks hold 180 litres and 135 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  6. 6.Find the smallest number bigger than 15 that leaves a remainder of 6 when divided by 15, 12 or 9.
  7. 7.Nisha takes 54 seconds and Rahul takes 90 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  8. 8.Three temple bells ring every 4, 5 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  9. 9.Find the smallest number bigger than 8 that leaves a remainder of 1 when divided by 3, 8 or 6.
  10. 10.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 5, 4 or 12.
  11. 11.Find the smallest number bigger than 8 that leaves a remainder of 2 when divided by 6, 8 or 4.
  12. 12.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 3, 9 or 10.
  13. 13.Three temple bells ring every 8, 6 and 18 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  14. 14.A hall floor is 480 cm long and 420 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  15. 15.Find the smallest number bigger than 12 that leaves a remainder of 2 when divided by 8, 12 or 9.
  16. 16.Two tanks hold 315 litres and 405 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  17. 17.Find the smallest number bigger than 5 that leaves a remainder of 2 when divided by 5, 3 or 4.
  18. 18.Two tanks hold 240 litres and 280 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  19. 19.Priya takes 30 seconds and Kabir takes 48 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  20. 20.Find the smallest number bigger than 9 that leaves a remainder of 3 when divided by 5, 9 or 6.
  21. 21.Vivaan takes 48 seconds and Kavya takes 36 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  22. 22.Ananya takes 36 seconds and Aarav takes 45 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  23. 23.Two tanks hold 100 litres and 80 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  24. 24.Two tanks hold 280 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  25. 25.Arjun takes 48 seconds and Aarav takes 90 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  26. 26.Find the smallest number bigger than 12 that leaves a remainder of 1 when divided by 6, 12 or 3.
  27. 27.A hall floor is 180 cm long and 135 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  28. 28.A hall floor is 200 cm long and 120 cm wide. It is covered with the largest square tiles that fit exactly. How many tiles are needed?
  29. 29.Three temple bells ring every 8, 6 and 10 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  30. 30.Two tanks hold 315 litres and 360 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  31. 31.Three temple bells ring every 30, 15 and 4 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  32. 32.Priya takes 45 seconds and Aditya takes 30 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  33. 33.Find the smallest number bigger than 9 that leaves a remainder of 2 when divided by 6, 5 or 9.
  34. 34.Priya takes 80 seconds and Kavya takes 72 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  35. 35.Find the smallest number bigger than 10 that leaves a remainder of 1 when divided by 6, 10 or 8.
  36. 36.Two tanks hold 150 litres and 240 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  37. 37.Two tanks hold 405 litres and 90 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?
  38. 38.Saanvi takes 60 seconds and Isha takes 48 seconds to run once round a track. They start together from the start line. After how many seconds will they first be at the start line together again?
  39. 39.Three temple bells ring every 24, 10 and 8 minutes. They ring together at 9:00 am. After how many minutes will they next ring together?
  40. 40.Two tanks hold 270 litres and 120 litres of milk. What is the biggest can (in litres) that can empty both tanks exactly, with no milk left over?

Answer key

  1. 150
  2. 31
  3. 10
  4. 42
  5. 45
  6. 186
  7. 270
  8. 40
  9. 25
  10. 62
  11. 26
  12. 91
  13. 72
  14. 56
  15. 74
  16. 45
  17. 62
  18. 40
  19. 240
  20. 93
  21. 144
  22. 180
  23. 20
  24. 40
  25. 720
  26. 13
  27. 12
  28. 15
  29. 120
  30. 45
  31. 60
  32. 90
  33. 92
  34. 720
  35. 121
  36. 30
  37. 45
  38. 240
  39. 120
  40. 30

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